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Fraction to decimal

Turn a fraction into a decimal and see exactly which digits repeat, and how many at a time. Free, with no account or uploads.

Turn a fraction into a decimal

Type the fraction. A decimal that repeats is shown with a line over the digits that come round again.

Which way?
Decimal to fractionFraction to decimal

1/7 as a decimal

0.(142857)

The digits under the line repeat for ever: 6 digits at a time

How it is worked out

  1. Divide the top by the bottom: 1 ÷ 7.\frac{1}{7} = 0.\overline{142857}
  2. The remainders come round again after 6 digits, so the digits repeat from there. A fraction's decimal ends only when its bottom, simplified, has no prime factors but 2 and 5.
How it works and help
Every fraction is kept exact, step by step, on your device. Nothing you type is sent anywhere.

A little help along the way

Follow these steps. Everything is worked out exactly in your browser; nothing is sent anywhere.

  1. Say what you want to doWork with fractions is the usual. The others simplify a ratio, find x or share out a total, turn decimals and fractions into each other, and work with picture sizes.
  2. Type the numbersFractions as 3/4, mixed numbers as 1 1/2, ratios with colons as 12 : 18, and repeating decimals with brackets as 0.1(6).
  3. Read the answer and every stepThe answer is drawn as a textbook would, with each step under it.

Questions people ask

Why does 1/3 never end as a decimal?
A fraction's decimal ends only when its bottom, simplified, has no prime factors but 2 and 5. Three is not one of them, so the division never comes out even and the 3s repeat for ever.
How long can the repeating part be?
Up to one less than the bottom: 1/7 repeats 142857, six digits, and 1/97 repeats 96 digits. The page finds the repeat exactly by watching for a remainder it has seen before.
How is the repeat shown?
With a line over the digits that repeat, and in the bracket form 0.(142857) that you can copy and type back in.

This page is the Fraction and ratio calculator, opened for this one job; every other tool it has is one press away. Each of its settings is explained on the Fraction and ratio calculator's own page.

Read the step-by-step guide

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